ON QUANTUM FLAG ALGEBRAS

Let G be a semisimple simply connected algebraic group over an algebraically closed field of characteristic 0. Let V be a simple finite-dimensional G-module and let y be its highest weight vector. It is a classical result of B. Kostant that the algebra of functions on the closure of G . y is quadratic. In this paper we generalize this result to the case of the quantum group U-q(g). The proof uses information about the quantum R-matrix due to Drinfeld and Reshetikhin.